Suppose that X1, , Xm form a random sample from the normal distribution with mean1 and variance 2, and Y1, , Yn form an independent random sample from the normal distribution with mean 2 and variance 22 Let a For what pairs of values of and is S2X S2Y an unbiased estimator of 2 b Determine the valu...

a ES 2 X S 2 Y m 1 2 n 12 2 Hence this estimator will be unbiased if m 1 2n 1 1 b Since S 2 X and ...

Suppose that X1, . . . , Xm form a random sample from the normal distribution with

Question:

Suppose that X1, . . . , Xm form a random sample from the normal with meanμ1 and variance σ2, and Y1, . . . , Yn form an independent random sample from the normal with mean μ2 and variance 2σ2. Let
a. For what pairs of values of α and β is αS2X + βS2Y an unbiased estimator of σ2?
b. Determine the values of α and β for which αS2X + βS2Y will be an unbiased estimator with minimum variance.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...